| Title: | Commuting graphs and extremal centralizers |
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| Authors: | ID Dolinar, Gregor (Author)
ID Guterman, Aleksandr Èmilevič (Author)
ID Kuzma, Bojan (Author)
ID Oblak, Polona (Author) |
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| Files: |  RAZ_Dolinar_Gregor_i2014.pdf (228,78 KB)
MD5: 9CDB04635DE21D9AE1CDED8FF95C0278
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| Language: | English |
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| Work type: | Unknown |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | We determine the conditions for matrix centralizers which can guarantee the connectedness of the commuting graph for the full matrix algebra ▫$M_n(\mathbb{F})$▫ over an arbitrary field ▫$\mathbb{F}$▫. It is known that if ▫$\mathbb{F}$▫ is an algebraically closed field and ▫$n \ge 3$▫, then the diameter of the commuting graph of ▫$M_n(\mathbb{F})$▫ is always equal to four. We construct a concrete example showing that if ▫$\mathbb{F}$▫ is not algebraically closed, then the commuting graph of ▫$M_n(\mathbb{F})$▫ can be connected with the diameter at least five. |
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| Keywords: | commuting graph, matrix ring, centralizer |
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| Year of publishing: | 2014 |
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| Number of pages: | str. 453-459 |
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| Numbering: | Vol. 7, no. 2 |
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| PID: | 20.500.12556/RUP-17610  |
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| UDC: | 519.17:512.6 |
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| ISSN on article: | 1855-3966 |
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| COBISS.SI-ID: | 16868441 |
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| Publication date in RUP: | 30.12.2021 |
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| Views: | 1117 |
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| Downloads: | 27 |
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| Metadata: |    |
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